The factor analytic approach paved the way for, what seemed to many in the social and psychological sciences, an objective and quantitative framework for measuring unobservable  hypothetical constructs such as “self-esteem”, “verbal ability”, and “quality of life”. Indeed Spearman's single factor model, in which both the one latent variable and the observed variables are assumed continuous, has laid the foundation for a long research program in psychometrics that has spanned well over a century. To account for the inadequacy of a single factor to account for the covariance pattern in testing data, the psychologist Thurstone extended the single factor model to multiple factors [1]}. The factor model was constantly refined and generalized, culminating in the structural equation model introduced by [2]} in which linear structural relationships between the latent variables are also modeled. In educational testing, item response theory models [3]} were developed to accommodate categorical observed variables encountered in testing in which test items assume two values, correct and incorrect. In sociology, clustering analysis motivated the development of latent class models (i.e. mixture models) in which the latent variables are assumed to be categorical [4]}. Since then, a large body of work has been built on top of these foundational early advances and many authors [5]}, [6]}, [7]} have attempted to bring together the various models under one roof in a general framework. The most encompassing as of yet is the Generalized Linear Latent and Mixed model (GLLMM) introduced by [8]} as a unified general framework that brings together not just factor analysis, IRT, structural equations, and latent class models commonly encountered in psychometrics and social quantitative methods, but also mainstream statistical random effects models such as multilevel regression, and longitudinal models.
